Do i have to take shoes off inside if I played games or ate there or

Ok

No

There is no issue in the pub area. If shoes are wet or snow covered we request for the safety of our bowlers that you either dry them or remove them.

Not if you don't go in the bowling area

The food/bar area is before the bowling area so good there. The arcade area is just around the corner by restrooms so I imagine they don't disallow bar/restaurant guests from using the bathroom and so yes you'd be able to get to the arcade fine. If you mean bowl when you say games then you obviously have to change into bowling shoes for that area, but I assume you mean arcade games.